PRP Records

Probable Primes Top 10000

(271023 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9751(2^230746+3114)/269462Stefano Morozzi01/2020
97525^99359-2^9936069449Mike Oakes12/2010
9753(29*2^230684+1)/139569442Lelio R Paula08/2012
975417692^8411+8411^1769269439Hans Havermann09/2019
9755(2^230638+1278)/269429Stefano Morozzi01/2020
9756(19*10^69424+77)/369425Robert Price08/2016
9757(2^230610+1222)/269421Stefano Morozzi01/2020
975819^54287-9669420Lelio R Paula09/2013
975920739^2222+2222^2073969409Hans Havermann09/2019
97612^230541+5890569400Lelio R Paula04/2012
9760(2^230540+2818)/269400Stefano Morozzi01/2020
97622^230506+1270569390Lelio R Paula02/2013
97638*6^89156-569378Lelio R Paula09/2014
9764(18815^16231-1)/1881469376Serge Batalov08/2020
9765(2^230443+3594)/269370Stefano Morozzi01/2020
97662^230438-11134769369Enzo Doria05/2014
9767(2^230434+3150)/269368Stefano Morozzi01/2020
97682^230428-9969366Lelio R Paula02/2012
9769(62^38699+1)/6369362Paul Bourdelais08/2017
9770(2^230413+3090)/269361Stefano Morozzi01/2020
97713*10^69354+1769355Robert Price03/2017
9772(493*10^69340-7)/969342Robert Price07/2016
9773(2^230325+590)/269335Stefano Morozzi01/2020
9775(41*10^69321+373)/969322Robert Price04/2017
9774(2^230282+1990)/269322Stefano Morozzi01/2020
97766^89072+5369312Lelio R Paula09/2013
9777155^31639+269300Lelio R Paula05/2013
9778(2^230117+3462)/269272Stefano Morozzi01/2020
9779(16941^16381-1)/1694069271Serge Batalov08/2020
97803*7^81965-469269Lelio R Paula09/2014
9781(16*10^69265+41)/369266Robert Price10/2017
9782(86*10^69260-77)/969261Robert Price05/2016
97839*5^99087+469260Lelio R Paula09/2014
97843^145145+266069252Lelio R Paula09/2013
978511^66492-114069245Enzo Doria11/2012
97865*3^145129-469245Lelio R Paula04/2014
97877*3^145126+869244Lelio R Paula04/2014
978811^66480-237069232Enzo Doria12/2012
9789(2^229965+3482)/269227Stefano Morozzi01/2020
9790(2^229968+3010)/269227Stefano Morozzi01/2020
9791(22589^15901-1)/2258869227Serge Batalov08/2020
97922^229962-6569226Lelio R Paula02/2012
97932^229958-11073369225Enzo Doria05/2014
9794V(332407)69225Serge Batalov03/2015
97956^88959+769224Lelio R Paula09/2013
979615^58855-9469219Lelio R Paula09/2013
9797(2^229941+774)/269219Stefano Morozzi01/2020
9798(2^229931+3270)/269216Stefano Morozzi01/2020
9799159773#-p(159773)69212Henri Lifchitz12/2018
980020223^2638+2638^2022369189Hans Havermann09/2019
9802(2^229838+47)/1208169185Lelio R Paula04/2012
9801(2^229828+3810)/269185Stefano Morozzi01/2020
98033^144952+9869160Lelio R Paula09/2013
98045^98941-7269157Lelio R Paula06/2013
980563329!4+25669147Robert Price09/2019
980616422^16229+16229^1642269142Hans Havermann09/2019
9807(17*2^229604-1)/22969117Lelio R Paula01/2014
98082^229585-106369112Yves Minet11/2012
9809(13*2^229567-1)/1969107Lelio R Paula01/2014
9810(2^229419+1946)/269062Stefano Morozzi01/2020
9811(2^229399+1890)/269056Stefano Morozzi01/2020
9812(13*2^229393-1)/569055Lelio R Paula01/2014
9813(2^229388+3666)/269053Stefano Morozzi01/2020
9814(53*10^69050-17)/969051Robert Price09/2015
9815(3887^19237-1)/388669050Serge Batalov08/2020
9816(43*10^69048+47)/969049Robert Price12/2017
9817(6420^18131-1)/641969031Serge Batalov08/2020
98182^229305-186853369028Enzo Doria04/2016
98192^229297+138569026Lelio R Paula04/2012
982018^54986-244169023Enzo Doria03/2013
9821(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
98225^98736-1463669014Enzo Doria02/2013
9823(2^229252+2346)/269012Stefano Morozzi01/2020
9825(13^61949-5^61949)/869007Robert Price03/2013
9824(2^229235+2966)/269007Stefano Morozzi01/2020
9826(2^229227+5)/61169002Lelio R Paula04/2012
98272^229216-11327969001Enzo Doria07/2014
982810^68994+5191368995Patrick De Geest03/2016
983010^68994-10^5814-168994Serge Batalov01/2011
982910^68994-8294768994Patrick De Geest03/2016
9831(2^229182+814)/268991Stefano Morozzi01/2020
9833(17*2^229136-1)/238168975Lelio R Paula01/2014
9832(6081^18229-1)/608068975Serge Batalov08/2020
98342^229113+10768970Lelio R Paula02/2012
983516877^12198+12198^1687768965Hans Havermann09/2019
9836(2^229056+2010)/268953Stefano Morozzi01/2020
983711^66202-441068943Enzo Doria01/2013
983812^63883+568942Lelio R Paula07/2013
9840(9913*2^229002-1)/39990368935Lelio R Paula04/2015
9839(2^228997+2454)/268935Stefano Morozzi01/2020
9841(2^228982+3118)/268931Stefano Morozzi01/2020
9842(2^228982+3490)/268931Stefano Morozzi01/2020
98432^228962-11158168925Enzo Doria05/2014
98442^228944+8168920Henri Lifchitz01/2007
984511^66174-5468914Lelio R Paula09/2013
9846(2^228926+694)/268914Stefano Morozzi01/2020
984716756^12959+12959^1675668911Hans Havermann09/2019
98482^228913-11126568910Enzo Doria05/2014
984918917^4392+4392^1891768909Hans Havermann09/2019
98512^228902+7351968907Enzo Doria04/2016
9850(2^228903+3018)/268907Stefano Morozzi01/2020
9852(2^228892+3046)/268904Stefano Morozzi01/2020
9853(47*2^228884+1)/6368901Lelio R Paula04/2015
9854(2^228857+3782)/268893Stefano Morozzi01/2020
9855(20337^15991-1)/2033668890Serge Batalov08/2020
985616542^14591+14591^1654268883Hans Havermann09/2019
98572^228821+7642768882Enzo Doria05/2016
9858(2^228798+442)/268875Stefano Morozzi01/2020
9859(2^228784+1222)/268871Stefano Morozzi01/2020
98603^144340+5068868Lelio R Paula09/2013
9861(2^228766+3850)/268866Stefano Morozzi01/2020
98622^228758-11296768864Enzo Doria06/2014
98632^228743-11137968859Enzo Doria05/2014
98642^228741-11091168858Enzo Doria05/2014
9866lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
98653*5^98511-868857Lelio R Paula09/2014
98672^228717+46768851Lelio R Paula02/2011
9868(2^228714+2110)/268850Stefano Morozzi01/2020
9870Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
9869(32933^15241-1)/3293268849Serge Batalov08/2020
9871(2^228704+3990)/268847Stefano Morozzi01/2020
9872(509203*2^228665-1)/3568840Lelio R Paula04/2015
9873(2^228648+2910)/268830Stefano Morozzi01/2020
98748^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
9875(2^228580+3762)/268810Stefano Morozzi01/2020
987611^66074-105068809Enzo Doria11/2012
9877(68*10^68798-11)/368800Robert Price10/2017
98782^228484+18168781Lelio R Paula02/2012
98792^228479-5869568780Lelio R Paula04/2012
98802^228465-1585368775Enzo Doria04/2013
988111^66040-540068774Enzo Doria01/2013
9882(13*2^228441-1)/57568766Lelio R Paula01/2014
9883(12170^16831-1)/1216968756Serge Batalov08/2020
9884(5683^18313-1)/568268754Serge Batalov08/2020
9885(17*2^228393+1)/29568752Lelio R Paula08/2012
988617859^7072+7072^1785968749Hans Havermann09/2019
9887(2^228368+1950)/268746Stefano Morozzi01/2020
98882*10^68744+4168745Robert Price01/2017
988911^66011-15068744Enzo Doria08/2012
9890(2^228307+3570)/268727Stefano Morozzi01/2020
9891(13*2^228304-1)/8168726Lelio R Paula01/2014
98922^228295-11107968724Enzo Doria05/2014
9894(3^144039+7)/2268723Lelio R Paula04/2012
9893(8*10^68722+49)/368723Robert Price03/2016
9895(35*10^68718+1)/968719Serge Batalov11/2010
98962^228271-22827168717Henri Lifchitz11/2004
98972^228257+8287568713Lelio R Paula02/2013
98983^144013+4068712Lelio R Paula09/2013
989913^61671-8668699Lelio R Paula09/2013
9900(46*10^68698+683)/968699Robert Price12/2017
990117^55828-7268694Lelio R Paula09/2013
990218675^4762+4762^1867568683Hans Havermann09/2019
99036^88259+6168679Lelio R Paula09/2013
990418^54699-568663Lelio R Paula09/2013
990533^45216+268662Lelio R Paula05/2013
9907(2^228073-5)/368657Lelio R Paula04/2012
9906(2^(6*38012+1)-5)/368657Kevin Acres11/2013
9908(17929^16141-1)/1792868653Serge Batalov08/2020
99092^228055-11160768652Enzo Doria05/2014
99102^228054-11476168652Enzo Doria05/2015
99112^228041+118568648Lelio R Paula04/2012
99122^228040-103768647Yves Minet11/2012
99132*F(328450)-168642Henri Lifchitz12/2009
99145^98201-3468640Lelio R Paula06/2013
9915(2^227993+1682)/268633Stefano Morozzi01/2020
9916(2^227989+842)/268632Stefano Morozzi01/2020
9917(2^227989+2010)/268632Stefano Morozzi01/2020
9918(2^227959+3614)/268623Stefano Morozzi01/2020
9919(2^227961+2054)/268623Stefano Morozzi01/2020
99209^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
9921(2^227938+3678)/268616Stefano Morozzi01/2020
992218177^5948+5948^1817768607Hans Havermann09/2019
9923(29257^15361-1)/2925668602Serge Batalov08/2020
9924(2^227869+2822)/268596Stefano Morozzi01/2020
9925(25910^15541-1)/2590968586Serge Batalov08/2020
9926(29779^15331-1)/2977868586Serge Batalov08/2020
9927(2^227813+666)/268579Stefano Morozzi01/2020
99287*2^227780-368570Lelio R Paula04/2014
992915327^16382-16382^1532768567Norbert Schneider11/2018
9930(2^227771+2730)/268566Stefano Morozzi01/2020
99312^227733-12168555Lelio R Paula02/2012
993216460^14607+14607^1646068549Hans Havermann09/2019
99332^227702-1696768546Enzo Doria05/2013
99342^227689-11165568542Enzo Doria05/2014
9935gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
99365^98051+268535Ray Chandler07/2011
99375*10^68524+5168525Robert Price01/2017
9938(11*10^68520-149)/368521Robert Price01/2017
993916624^13235+13235^1662468520Hans Havermann09/2019
994016359^15430+15430^1635968518Hans Havermann08/2019
994119^53573-7868507Lelio R Paula09/2013
9942(68*10^68504+13)/968505Ray Chandler10/2010
99439*5^98003+468503Lelio R Paula09/2014
994421121^1750+1750^2112168497Hans Havermann10/2019
99452^227528+5168493Lelio R Paula02/2012
9946(146*28^47316+1)/368476Karsten Bonath06/2018
9947(2^227462+3102)/268473Stefano Morozzi01/2020
99483^143497+868466Lelio R Paula04/2012
99492^227430-9568464Lelio R Paula02/2012
9950(8*10^68455+13)/368456Robert Price11/2017
99513*5^97934-268454Lelio R Paula09/2014
995220^52613+7768452Lelio R Paula09/2013
99532^227371+3276968446Lelio R Paula04/2012
9954(3^143465+4)/2127042006768440Lelio R Paula04/2012
9955CopelandErdos(68433)68433Eric W. Weisstein08/2013
99562^227323+7543168432Enzo Doria04/2016
99572^227314-196568429Lelio R Paula04/2012
99582^227303-11061768426Enzo Doria05/2014
99607^80963+6668422Lelio R Paula07/2013
99592^227290+7384968422Enzo Doria04/2016
9961(14^59693-1)/1368415Paul Bourdelais06/2008
9962(1838^20959-1)/183768415Serge Batalov08/2020
99632^227256-278624968411Enzo Doria03/2016
99658*10^68400-768401Dmitry Domanov11/2010
9964(15*2^227228-1)/58368401Lelio R Paula01/2014
99662^227210+186916968398Enzo Doria05/2016
9967(2^227176+2958)/268387Stefano Morozzi01/2020
99682^227159-183863568382Enzo Doria05/2015
996944*10^68368+368370Robert Price08/2017
99702^227115-780768369Lelio R Paula10/2009
997118469^5032+5032^1846968368Hans Havermann08/2019
99722^227078-4735568358Lelio R Paula04/2012
997316927^10920+10920^1692768355Hans Havermann10/2019
9974(2^227063-1017)/34968351Lelio R Paula04/2012
99752^227057+14809168351Lelio R Paula04/2012
99762^227046+18768348Lelio R Paula02/2012
9977(2^227030+454)/268343Stefano Morozzi01/2020
9978(2^227022+2950)/268341Stefano Morozzi01/2020
99802^227009-469368337Yves Minet05/2019
9979(2^227010+3214)/268337Stefano Morozzi01/2020
99819*10^68331+5968332Robert Price10/2017
998211^65608-72068324Enzo Doria11/2012
9983(32*10^68320+319)/968321Robert Price10/2017
998433408!2-2^33408-168315Joe McLean05/2017
99852*10^68311-9168312Robert Price04/2020
99862^226894-12368302Lelio R Paula02/2012
998710^68297+14155968298Patrick De Geest05/2013
998810^68297-9368297Robert Price05/2011
9989680^24107-679^2410768284Jean-Louis Charton07/2010
999012^63267+5968277Lelio R Paula07/2013
99912^226785-115968270Yves Minet11/2012
99927^80769+9068258Lelio R Paula07/2013
9993(88*10^68256-1)/368258Robert Price10/2017
99942^226741+6658768256Yves Minet10/2010
99952^226720-11240368250Enzo Doria06/2014
9996(78557*2^226694+1)/368247Lelio R Paula06/2014
9997(2^226665+1674)/268233Stefano Morozzi01/2020
9998(83*10^68231+7)/968232Robert Price10/2015
999965^37636+1668231Lelio R Paula01/2016
100005^97615-4^(97615+1)68230Robert Price04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

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